Wideband Modeling and Characterization of Differential Through-Silicon Vias for 3-D ICs

This paper presents the wideband modeling and analysis of differential through-silicon vias (D-TSVs) in 3-D ICs. An equivalent-circuit model of the ground-signal-signal-ground-type D-TSVs is given and validated against a commercial full-wave electromagnetic simulation tool. The common- and differential-mode impedances are extracted using the partial-element equivalent-circuit method, while the admittances are calculated analytically, with the MOS effects considered and treated appropriately. The circuit model can also be used for studying the differential annular TSVs (ATSVs). It is shown that the ATSVs are more suitable for transmitting differential signals in comparison with the cylindrical TSVs. Based on the equivalent-circuit model, the characteristic impedances and the forward transmission coefficients of the D-TSVs made of Cu and carbon nanotubes are characterized and compared under different settings of frequencies and temperatures.

I. Introduction

The 3-D IC is paving a potential path toward More-than-Moore technologies, since it offers another dimension by stacking functional blocks vertically [1]. As a key component in 3-D IC, through-silicon via (TSV), which is a high aspect ratio vertical interconnect providing connectivity between active layers, has attracted a lot of research interests in the past decade [2]. Recently, a number of studies are devoted to the electrical modeling and fabrication technologies for TSVs [3]–[8]. For example, Xu et al. [4] proposed a comprehensive compact resistance–inductance–capacitance–conductance model for ground–signal (GS)-type TSVs, with the consideration of the MOS effects.